By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.

Emmanuel Levinas has provided the philosophical basis for psychologies commensurate with the ethical basis of human existence; however, introducing psychologists to his work is frustrated by a number offactors. One of these factors is his use of theistic language in his philosophical writings. Two problems are discussed regarding this language. First, contemporary psychology, including the area ofpsychology of religion, rejects any theistic language as incompatible with an empirical science. Second, it is suggested that many persons, including psychologists, are not in (...) the cognitive developmental stage at which they can understand Levinas’s writings about God. Further, it is also suggested that psychology’s history warns against creating a psychological school or division based in Levinas’s thought. The article concludes with general discussion regarding how psychology can apply Levinas’s thought while leaving God and Levinas behind. (shrink)

We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.

A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...) a certain "slowness" property whereby the elements must enter X slowly (under a certain precise complexity measure of speed of computation) even though X may have high information content. Second we prove that every X with this slowness property is computable in some member of any nontrivial orbit, namely for any noncomputable A ∈ ε there exists B in the orbit of A such that X ≤ T B under relative Turing computability (≤ T ). We produce B using the Δ 0 3 -automorphism method we introduced earlier. (shrink)

We deal with the consistency strength of ZFC + variants of MA + suitable sets of reals are measurable (and/or Baire, and/or Ramsey). We improve the theorem of Harrington and Shelah [2] repairing the asymmetry between measure and category, obtaining also the same result for Ramsey. We then prove parallel theorems with weaker versions of Martin's axiom (MA(σ-centered), (MA(σ-linked)), MA(Γ + ℵ 0 ), MA(K)), getting Mahlo, inaccessible and weakly compact cardinals respectively. We prove that if there exists r (...) ∈ R such that ω L[ r] 1 = ω 1 and MA holds, then there exists a ▵ 1 3 -selective filter on ω, and from the consistency of ZFC we build a model for ZFC + MA(I) + every ▵ 1 3 -set of reals is Lebesgue measurable, has the property of Baire and is Ramsey. (shrink)

While there is a history of sorts clearly evident in the Preliminaries of James Harrington's Commonwealth of Oceana, one can hardly escape noticing the model qualities of the Commonwealth as it is proposed. Accepting this apparent dualism as an obstacle, Pocock has noted that Oceana cannot be understood as utopia unless first understood as history. Others would not necessarily agree. Yet, given that Harrington located his explanation for the dissolution of the government upon the failure of the nobility (...) to maintain English arms in time of crisis, I argue that in seeking a solution he turned to a series of debates regarding the history of the contemporary alternative to those failed feudal armies, the English militia. Having identified a crisis of arms, Harrington found tactical models dealing with the organization of a militia -- both contemporary and ancient -- to be a perfect historical model for his own commowealth. Considered in this context, the utopian status of the Commonwealth's orders becomes questionable and the work appears much more historical throughout. (shrink)